Про існування розв’язку задачі Коші для нелінійного дифузійного стохастичного диференціально-різницевого рівняння нейтрального типу в частинних похідних з урахуванням випадкових зовнішних збурень

The question related to the existence of the Cauchy problem solution in the class of nonlinear diffusion stochastic partial differential-difference equations of a neutral type with random external disturbances which are independent from the Wiener process is considered. Sufficient conditions are obt...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Datum:2017
Hauptverfasser: Yasynskyy, V. K., Yurchenko, I. V.
Format: Artikel
Sprache:Ukrainisch
Veröffentlicht: The National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute" 2017
Schlagworte:
Online Zugang:http://journal.iasa.kpi.ua/article/view/108824
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Назва журналу:System research and information technologies

Institution

System research and information technologies
Beschreibung
Zusammenfassung:The question related to the existence of the Cauchy problem solution in the class of nonlinear diffusion stochastic partial differential-difference equations of a neutral type with random external disturbances which are independent from the Wiener process is considered. Sufficient conditions are obtained for the diffusion coefficients of nonlinear stochastic differential-difference equations of a neutral type (NDSDRRNT) that guarantee the existence of the solution with the probability of 1. The method of the proof is based on the results of O.M. Stanzhitsky and A.O. Tsukanova on the existence and uniqueness of the Cauchy problem solution for the stochastic differential reaction-diffusion equation of a neutral type. In this paper, we prove the existence of a "mild solution" of NDSDRRNT. In some cases, such equations are mathematical models of real processes, the consideration of which is planned in the future work.